limit as x approaches infinity of [xsin(1/x)]

Lösung

x \to \infty lim ([x sin (\frac{1}{x})])

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Schritte zur Lösung

x \to \infty lim (x sin (\frac{1}{x}))

Umformung für L'Hopital

= x \to \infty lim (\frac{sin ( \frac{1}{x} )}{\frac{1}{x}})

Wende das L'Hopital Theorem an

= x \to \infty lim \frac{- \frac{c o s ( \frac{1}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}}

Vereinfache

\frac{- \frac{c o s ( \frac{1}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}} : cos (\frac{1}{x})

= x \to \infty lim (cos (\frac{1}{x}))

Wende die Kettenregel für Grenzen an:

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= 1

x \to (0) lim (\frac{1 - 1 + x y}{x y})

x \to 0 lim (+ \frac{1}{x})

x \to 3 lim (\frac{3 - 12 - x}{x - 3})

θ \to 0 lim (sin (θ) cot (2 θ))

x \to 0 + lim (tan (9 x))